Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Linking dynamic economic and ecological general equilibrium models

Although ecosystems provide myriad services to economies, only one service is considered in most renewable-resource models. The general equilibrium bioeconomic model introduced here admits a second service, and more importantly it accounts for how the two services are impacted by interactions within an eight-species ecosystem and interactions within a regional economy. Endangered Steller sea lion recovery measures via alternative pollock quotas change all ecosystem populations and all economic variables. While non-use values associated with the ecosystem (e.g., existence values) are not considered, all species matter for the economy because they are all used indirectly as support for ecosystem services. Regional welfare changes from reduced quotas show the tradeoff between consumptive and non-consumptive uses of the ecosystem.     

Market and underground activities in a two-sector dynamic equilibrium model

Summary. In this paper a two sector dynamic general equilibrium model is developed in order to evaluate the implications of the underground economy from a business cycle perspective. There are three main results. First, introducing an underground sector improves the fit of the model to the data, especially along several important labor market dimensions. Second, the model produces substantial internal propagation of temporary shocks. Third, it is shown that underground activities offer risk sharing opportunities by allowing households to smooth income through a proper labor allocation between the two sectors.Received: 17 June 2002, Revised: 25 April 2003, JEL Classification Numbers: E320, E260, J22, H200.We have benefited from the comments and suggestions of John Donaldson. We would also like to thank Paolo Siconolfi, Jean Pierre Danthine, Fausto Gozzi, Edmund Phelps, Gustavo Piga, Domenico Tosato, and the participants in the seminars at various universities, David Giles and Stefano Pisani for providing useful information on the underground data, Francesca Caponi for the comments and the information concerning the legal and fiscal aspects involved in the calibration, and Glenn Williams for the research assistance. Finally, we thank two anonymous referees for helpful comments on this and on earlier versions of the paper. Chiarini acknowledges financial support from the Ateneo Research fund of the University of Rome, La Sapienza, Dinamiche dell'integrazione europea e scelta di politica economica. All errors are ours. Correspondence to: F. Busato     

Effect of restricting asset trade in dynamic equilibrium models

Abstract. This paper shows that differences between the predictions of an international real business cycle model with complete markets and the predictions of a model where agents can trade only risk-free bonds depend heavily on three parameters: discount factor, and degrees of persistence and spillovers in productivity shocks. This sensitivity explains apparently paradoxical results previously obtained in the literature. Also, since empirical work finds that two of those parameters are not estimated precisely, the outcomes of quantitative studies comparing complete-markets and bond economies using only the point estimates of those parameters inherit the substantial uncertainty in the parameter estimates.     

Stability, global dynamics and Markov equilibrium in models of endogenous economic growth

This paper studies the local and global dynamics of two-sector models of endogenous growth with economy-wide external effects and taxes on capital and labor. The local analysis classifies the parameter space depending on the number of stationary solutions and local stability of equilibria. The global analysis shows that if taxes are within certain bounds and the size of the external effects on the average level of human capital is smaller than the share of physical capital, the equilibrium path is monotone and therefore a continuous Markov equilibrium can be constructed.     

Potential economic reforms in North Korea: a dynamic general equilibrium model

We use a dynamic general equilibrium model to examine hypothetical market reforms in North Korea. We model partial reform, in which producers choose capital allocations across sectors, with the government still fixing total capital. We also consider two full market reform scenarios. In one, public infrastructure investment remains unchanged, while, in the other, it increases substantially. In all scenarios, we assume a closed economy and a constant military size. Our simulations show little hope for the North Korean economy without boosting infrastructure. Although all of the reforms raise consumption, only significant increases in infrastructure investment bring positive economic growth.     

Non-computability of competitive equilibrium

Summary. We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]). Received: September 9, 1997; revised version: December 17, 1997     

Non-causal understanding with economic models: the case of general equilibrium

How can we use models to understand real phenomena if models misrepresent the very phenomena we seek to understand? Some accounts suggest that models may afford understanding by providing causal knowledge about phenomena via how-possibly explanations. However, general equilibrium models, for example, pose a challenge to this solution since their contribution appears to be purely mathematical results. Despite this, practitioners widely acknowledge that it improves our understanding of the world. I argue that the Arrow–Debreu model provides a mathematical how-possibly explanation which establishes claims of mathematical dependence. The account developed reveals how mathematical knowledge can inform claims about the world, allow ‘what-if-things-had-been-different’ inferences, and thus improve our understanding.     

Asset illiquidity and market shutdowns in competitive equilibrium

This paper introduces asymmetric information in a competitive asset market into a dynamic general-equilibrium model with borrowing constraints. In the presence of borrowing constraints, asset sales become a crucial means for agents to finance opportunities to invest in new assets. In this environment, reduced asset sales due to asymmetric information lower the economic growth rate if agents invest in new assets. The volume of asset trade, however, becomes zero if and only if agents stop investing in new assets because of sufficiently low aggregate productivity. A low economic growth rate with a market shutdown is solely due to low aggregate productivity without any role of the market shutdown.     

Learning competitive equilibrium in laboratory exchange economies

A laboratory market for two goods is instituted to examine the hypothesis that individuals will eventually coordinate on the induced competitive equilibrium. The mechanism for exchange strongly restricts the space of agent actions, facilitating the identification of decision rules. Evidence for learning competitive equilibrium is mixed due to strong heterogeneity in decision making. Some subjects forego immediately available gains when they expect the market to move in a more favorable direction, a condition necessary for coordinating on the competitive outcome. However, a majority do not, and many are content to satisfice, though the means to do better was reasonably transparent. I gratefully acknowledge the advice and tutelage of John Duffy and Stephen Spear, and would also like to thank David Grether, Dan Houser, Michael Peress, Bryan Routledge, Shyam Sunder, and participants at the Midwest Theory meetings (Bloomington) and the ESA regional meetings (Tucson) for useful feedback. Two patient and insightful anonymous referees have helped to greatly improve this paper and my future written endeavors. This project was financially supported by the Department of Economics at Carnegie Mellon University, the International Foundation for Research in Experimental Economics at George Mason University, and the Social and Information Sciences Laboratory at Caltech, as well as by Stephen Spear. Finally, special thanks is owed to Allen Geary, Jr. for co-developing the software used in these experiments, and to the Pittsburgh Experimental Economics Laboratory for use of its facilities.     

Growth responses to competitive shocks: Market structure dynamics under liberalisation

Liberalisation transforms market structures through the responses of incumbent firms and entrants to freedom of choice. Market shares tend to turn more volatile, and the agility and competitiveness of small, as against large, firms determine whether markets grow more concentrated, or less. We analyse the way these processes played out in Indian manufacturing industries over the 17-year period from 1981, spanning the domestic liberalisation of 1985 and the more comprehensive reforms of 1991. An observer looking at summary measures of market concentration might conclude that not much happened under either liberalisation episode. In fact, market share grew significantly more turbulent, and the relationship between market share-growth and initial share changed considerably. Domestic and comprehensive liberalisation saw different types of course corrections in these processes. But in both liberalisation episodes they tended to offset one another in their impact on observed market concentration, which therefore, changed little.     

Econometrics and equilibrium models

In Rational Econometric Man, Edward Nell and Karim Errouaki present a welcome and timely case for the view that econometrics and econometric model-building may not be the magic tools to solve all empirical questions despite what many seem to have thought they were in the 1960s. Here I examine some possible problems with econometric models that have to do with their usually taking the form of equilibrium models. Some of these problems were recognized by Trygve Haavelmo decades ago. And as Aris Spanos has recently discussed, the problems are often the result of what we say in our textbooks. Some problems have to do with what we mean by econometric parameters and others with how we use probabilities.     

On the uniqueness of competitive equilibrium

Summary . The paper is concerned with the following question: in addition to local uniqueness, what other conditions must be imposed to ensure global uniqueness of competitive equilibrium? The answer is provided within a standard framework involving excess demand functions. Conditions are identified which have the nice property that they are true close to a regular equilibrium. Uniqueness is established by considering an adjustment process and showing that under the mentioned conditions, every equilibrium is locally asymptotically stable and moreover the process itself is globally stable; uniqueness follows from an Arrow and Hahn (1971) result. Alternatively, the paper may be seen as identifying conditions under which there is a vectorfield satisfying the requirements of an uniqueness result due to Dierker (1974). Received: July 1, 1996; revised version October 7, 1996     

Unhedgeable shocks and statistical economic equilibrium

We develop a statistical concept of economic equilibrium as the stationary distribution of a random walk on the exchange equilibrium set (the contract set) of a pure exchange economy induced by unhedgeable shocks that perturb the economy from the exchange equilibrium set and subsequent disequilibrium trading that returns the economy to a new equilibrium. The Fokker–Planck equation for the resulting drift-diffusion process implies that the stationary distribution is independent of the size of the shock so that a small-disturbance limiting distribution is well defined. We present explicit solutions for the statistical equilibrium for the cases of quasilinear and Gorman-aggregatable Cobb–Douglas economies, and illustrate the results in the context of a generic dividend-discount model to emphasize the distinction between insurable risk and unhedgeable uncertainty in this context. The statistical equilibrium of income or wealth for quasilinear economies is described by an exponential Gibbs distribution. The statistical equilibrium income and wealth distributions for Gorman-aggregatable Cobb–Douglas economies can take a wider variety of forms, including power-law and gamma distributions. The statistical equilibria calculated for these examples suggest a close relation to widely observed statistical distributional regularities in real-world economies.     

Von neumann facets and the dynamic stability of perfect foresight equilibrium paths in neo-classical trade models

I am grateful to two anonymous referees for useful comments on an earlier version of this paper.